Questions tagged [separability]

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21
votes
4answers
4k views

Fast / Efficient Way to Decompose a Separable integer 2D Filter Coefficients without the SVD

I would like to be able to quickly determine whether a given 2D kernel of integer coefficients is separable into two 1D kernels with integer coefficients. E.g. ...
16
votes
3answers
420 views

Is ICA appropriate for separating mixed signals when all source signals are NOT detectable at all sensors?

A generic implementation of ICA for the separation of a mixture of $N$ signals into their $M$ constituent components requires that the signals be assumed to be a linear instantaneous mixture of the ...
8
votes
1answer
4k views

Why does the separable filter reduce the cost of computing the operator?

A separable filter in image processing can be written as product of two more simple filters. Typically a 2-dimensional convolution operation is separated into 2 onedimensional filters. This reduces ...
4
votes
1answer
815 views

How to Check Separability of 2D Signal / Matrix

suppose x(n1,n2) = {1 ,n1=0,n2=0 ; 2 ,n1=1,n2=0 ; 3 ,n1=0,n2=1 ; 6 ,n1=1,n2=1 } then, how do i prove it is separable.
2
votes
1answer
100 views

How to Decompose a Separable Filter?

I have done some research on the Internet and I have found that a given 2D mask is separable if it exists only a singular value of that matrix. For example, given the following matrix: $$A = \begin{...
2
votes
2answers
2k views

How Is Laplacian of Gaussian (LoG) Implemented as Four 1D Convolutions?

I am trying to understand the four 1D convolution operations involved in implementation of Laplacian of Gaussian(LoG). I have read this answer and I am also reading ...
2
votes
2answers
7k views

How to Prove a 2D Filter Is Separable?

I want to prove that 2D Gaussian filter is separable and we can separate it into two dimensions, my problem is about the size of filters. we should prove that $G(x,y)*I$(where $G(x,y)=$$\begin{bmatrix}...
2
votes
2answers
50 views

Mathematical Approach to Detect If a 2D Signal Is Separable

In the Special 2-D Sequences page the following examples are demonstrated, 2D dirac 2D diagonals 2D unit step function Is there a more defined method or series of steps for determining if a ...
2
votes
1answer
652 views

Normalized-cross correlation operation

According to my question about separability of Gabor filters in this link, I want now to convolve my image with this separable filter by using the normalized cross correlation operation. Assume my <...
1
vote
1answer
3k views

How to find out if a transform matrix is separable?

In image processing, when we have a series of basis images, how could we know if the transformation is separable or not? For example, I know that following bases are separable and transformation can ...
1
vote
1answer
3k views

How Does a Separable Filter Work?

I am new to signal processing, and was reading about filters. I came upon the sobel filter which has the following forms, From what I understand to apply this filter to a 2-d signal, place the ...
1
vote
1answer
39 views

Separability vs. Resolution - Synonymous terms?

In terms of discrete representation of a variable, let's say time measurements in absolute values in [seconds], is there a difference between separability and resolution? When do speak of either ...
1
vote
0answers
26 views

How to classify overlapped signals?

A known signal, signal 1 got overlapped with an unknown signal. Likewise, signal 2 overlapped with another unknown signal. The problem I face now is how to classify the overlapped signals based on the ...
0
votes
1answer
13 views

Rules of image's separability

We know separable convolution helps reduce number of calculations during convolution operation. As usual we see this separability is being applied on convolution kernels. Can't we apply this ...
0
votes
1answer
339 views

Fast/efficient way to compute Laplacian edge enhancement filter

I would like to implement a somewhat smarter Laplacian edge enhancement convolution. Right now it is implemented as (generic 3x3 convolution): ...
0
votes
1answer
20 views

The notation to express a datum filtered by arbitray number of one-dimensional filters?

I'm a pure novice in signal processing but I'm writing a paper that needs to be expressed in the SP way. The question is, I want to express an N-dimensional datum goes through N one-dimensional ...
0
votes
1answer
230 views

Octave: Poor performance of convolution by separable 1D kernels

As a newbie, I wrote a custom function in octave to perform a 2D image convolution using separable kernels. The results of this custom function were compared with conv2() and they were consistent. But ...